|GNU Octave Manual Version 3|
by John W. Eaton, David Bateman, Søren Hauberg
Paperback (6"x9"), 568 pages
RRP £24.95 ($39.95)
26.1 Evaluating Polynomials
The value of a polynomial represented by the vector c can be evaluated at the point x very easily, as the following example shows:
N = length(c)-1; val = dot( x.^(N:-1:0), c );
While the above example shows how easy it is to compute the value of a
polynomial, it isn't the most stable algorithm. With larger polynomials
you should use more elegant algorithms, such as Horner's Method, which
is exactly what the Octave function
In the case where x is a square matrix, the polynomial given by
c is still well-defined. As when x is a scalar the obvious
implementation is easily expressed in Octave, but also in this case
more elegant algorithms perform better. The
provides such an algorithm.
- Function File: polyval (c, x)
- Evaluate a polynomial.
polyval (c, x)will evaluate the polynomial at the specified value of x.
If x is a vector or matrix, the polynomial is evaluated at each of the elements of x.
See also polyvalm, poly, roots, conv, deconv, residue, filter, polyderiv, polyinteg
- Function File: polyvalm (c, x)
- Evaluate a polynomial in the matrix sense.
polyvalm (c, x)will evaluate the polynomial in the matrix sense, i.e. matrix multiplication is used instead of element by element multiplication as is used in polyval.
The argument x must be a square matrix.
See also polyval, poly, roots, conv, deconv, residue, filter, polyderiv, and polyinteg
|ISBN 095461206X||GNU Octave Manual Version 3||See the print edition|